Newton System Research Articles

A deconvolution method for scintillator gamma-ray spectrum analysis based on convex optimization

A deconvolution method based on convex optimization is developed and applied to gamma-ray spectrum deconvolution of simulated complicated spectra of NaI(Tl) measurements. The gamma-ray deconvolution problem is transformed into a minimization problem with inequality constraints. Then the Lagrange dual method is applied to transform the primal Lagrange problem into the dual problem. The interior-point method is applied and the logarithm barrier function is applied to construct the Newton system for iteration search. PCG (Preconditioned Conjugate Gradient) is applied to do the inexact search of the Newton system. The proposed method is applied to deconvolution of 4 typical gamma-ray spectra: (a) characteristic gamma-ray spectrum of 137Cs; (b) characteristic gamma-ray spectrum of 60Co; (c) characteristic gamma-ray spectrum of 152Eu; (d) mixed fission products in the primary loop of PWR (Pressurized Water Reactor), including the isotopes of Kr, Xe, I and Cs. Compared with the ML-EM method, improved accuracies and high resolution can be obtained with the proposed method. Moreover, the proposed method costs about 1/3 computational time of the ML-EM method.

TCT-199 The Newton System: An Innovative Weight Supporting Device for the Prevention of Lead Apron–Related Musculoskeletal Injuries

Interventional cardiologists’ use of lead aprons for radiation protection has led to numerous musculoskeletal problems. Efficient prevention methods are lacking. It has been shown that thermal imaging could be used to ascertain muscular fatigue when wearing lead aprons. Aim: The purpose was to

A corrector\u2013predictor interior-point method with new search direction for linear optimization

We introduce a feasible corrector–predictor interior-point algorithm (CP IPA) for solving linear optimization problems which is based on a new search direction. The search directions are obtained by using the algebraic equivalent transformation (AET) of the Newton system which defines the central path. The AET of the Newton system is based on the map that is a difference of the identity function and square root function. We prove global convergence of the method and derive the iteration bound that matches best iteration bounds known for these types of methods. Furthermore, we prove the practical efficiency of the new algorithm by presenting numerical results. This is the first CP IPA which is based on the above mentioned search direction.

Dynamic Non-diagonal Regularization in Interior Point Methods for Linear and Convex Quadratic Programming

In this paper, we present a dynamic non-diagonal regularization for interior point methods. The non-diagonal aspect of this regularization is implicit, since all the off-diagonal elements of the regularization matrices are cancelled out by those elements present in the Newton system, which do not contribute important information in the computation of the Newton direction. Such a regularization has multiple goals. The obvious one is to improve the spectral properties of the Newton system solved at each iteration of the interior point method. On the other hand, the regularization matrices introduce sparsity to the aforementioned linear system, allowing for more efficient factorizations. We also propose a rule for tuning the regularization dynamically based on the properties of the problem, such that sufficiently large eigenvalues of the non-regularized system are perturbed insignificantly. This alleviates the need of finding specific regularization values through experimentation, which is the most common approach in the literature. We provide perturbation bounds for the eigenvalues of the non-regularized system matrix and then discuss the spectral properties of the regularized matrix. Finally, we demonstrate the efficiency of the method applied to solve standard small- and medium-scale linear and convex quadratic programming test problems.

Commuting planar polynomial vector fields for conservative newton systems

We study the problem of characterizing polynomial vector fields that commute with a given polynomial vector field on a plane. It is a classical result that one can write down solution formulas for an ODE that corresponds to a planar vector field that possesses a linearly independent (transversal) commuting vector field (see Theorem 2.1). In what follows, we will use the standard correspondence between (polynomial) vector fields and derivations on (polynomial) rings. Let [MATH HERE] be a derivation, where f is a polynomial with coefficients in a field K of zero characteristic. This derivation corresponds to the differential equation ẍ = f ( x ), which is called a conservative Newton system as it is the expression of Newton's second law for a particle confined to a line under the influence of a conservative force. Let H be the Hamiltonian polynomial for d with zero constant term, that is [MATH HERE]. Then the set of all polynomial derivations that commute with d forms a K [ H ]-module M d [6, Corollary 7.1.5]. We show that, for every such d, the module M d is of rank 1 if and only if deg f ⩾ 2. For example, the classical elliptic equation ẍ = 6x 2 + a, where a ∈ C, falls into this category. For proofs of the results stated in this abstract, see [5].

Selective Pyragas control of Hamiltonian systems

We consider a Newton system which has a branch (surface) of neutrally stable periodic orbits. We discuss sufficient conditions which allow arbitrarily small delayed Pyragas control to make one selected cycle asymptotically stable. In the case of small amplitude periodic solutions we give conditions in terms of the asymptotic expansion of the right hand side, while in the case of larger cycles we frame the conditions in terms of the Floquet modes of the target orbit as a solution of the uncontrolled system.

Multiple positive solutions for a Schrödinger–Newton system with sign-changing potential

In this paper, we study the Schrödinger–Newton systems with sign-changing potential in a bounded domain. By using the variational method and analytic techniques, the existence and multiplicity of positive solutions are established.

Positive solutions for a nonlocal Schrödinger–Newton system involving critical nonlinearity

In this paper, we study the critical Schrödinger–Newton system with a nonlocal term, and establish the existence of multiple positive solutions via using variational method.

A generalized direction in interior point method for monotone linear complementarity problems

In this paper, we present a new interior point method with full Newton step for monotone linear complementarity problems. The specificity of our method is to compute the Newton step using a modified system similar to that introduced by Darvay in 2003. We prove that this new method possesses the best known upper bound complexity for these methods. Moreover, we extend results known in the literature since we consider a general family of smooth concave functions in the Newton system instead of the square root. Some computational results are included to illustrate the validity of the proposed algorithm.

A dual Newton strategy for scenario decomposition in robust multistage MPC

SummaryThis paper considers the solution of tree‐structured quadratic programs as they may arise in multistage model predictive control. In this context, sampling the uncertainty on prescribed decision points gives rise to different scenarios that are linked to each other via the so‐called nonanticipativity constraints. Previous work suggests to dualize these constraints and apply Newton's method on the dual problem to achieve a parallelizable scheme. However, it has been observed that the globalization strategy in such an approach can be expensive. To alleviate this problem, we propose to dualize both the nonanticipativity constraints and the dynamics to obtain a computationally cheap globalization. The dual Newton system is then reformulated into small highly structured linear systems that can be solved in parallel to a large extent. The algorithm is complemented by an open‐source software implementation that targets embedded optimal control applications.

Nonlinear behavior of a novel chaotic jerk system: antimonotonicity, crises, and multiple coexisting attractors

In this contribution, a novel Jerk system with a smooth piecewise quadratic nonlinearity is introduced. The new nonlinearity provides a similar smoothness as the cubic polynomial function, but a faster response and a simpler circuitry. The basic dynamical properties of the model are discussed in terms of its parameters by using standard nonlinear analysis tools including phase space trajectory plots, frequency spectra, bifurcation diagrams and Lyapunov exponent plots. The bifurcation analysis yields very rich and interesting scenarios such as period-doubling bifurcations, antimonotonicity (i.e. the concurrent creation and annihilation of periodic orbits), periodic windows, and symmetry recovering crises. One of the main findings of this work is the presence of a window in the parameter space in which the novel jerk system experiences the unusual and striking feature of multiple coexisting attractors (i.e. coexistence of four or six disconnected periodic and chaotic attractors) for the same parameters’ setting. Correspondingly, basins of attraction of various competing attractors display extremely complex basin boundaries. Compared to some lower dimensional systems (e.g. Leipnik–Newton system, modified Sprott B system) capable of displaying such type of behavior reported to date, the jerk system introduced in this work represents the simplest and the most ‘elegant’ paradigm. An electronic circuit for allowing an illustration of the theoretical model is proposed and implemented in PSpice. The results obtained in this work let us conjecture that there exist some regions in its parameter space (that need to be uncovered) in which the universal Chua’s circuit experiences six disconnected non static attractors similar to those presented in this work.

Generalized Schrödinger–Newton system in dimension N ⩾ 3: Critical case

In this paper we study a system which is equivalent to a nonlocal version of the well known Brezis Nirenberg problem. The difficulties related with the lack of compactness are here emphasized by the nonlocal nature of the critical nonlinear term. We prove existence and nonexistence results of positive solutions when N=3 and existence of solutions in both the resonance and the nonresonance case for higher dimensions.

The dynamics of the Schrödinger–Newton system with self-field coupling

We probe the dynamics of a modified form of the Schrödinger–Newton (SN) system of gravity coupled to single particle quantum mechanics. At the masses of interest here, the ones associated with the onset of ‘collapse’ (where the gravitational attraction is competitive with the quantum mechanical dissipation), we show that the Schrödinger ground state energies match the Dirac ones with an error of . At the Planck mass scale, we predict the critical mass at which a potential collapse could occur for the self-coupled gravitational case, Planck mass, and show that gravitational attraction opposes Gaussian spreading at around this value, which is a factor of two higher than the one predicted (and verified) for the SN system. Unlike the SN dynamics, we do not find that the self-coupled case tends to decay towards its ground state; there is no collapse in this case.

Stability of self-gravitating Bose-Einstein condensates

We study the ground state and the first three radially excited states of a self-gravitating Bose-Einstein- Condensate with respect to the influence of two external parameters, the total mass and the strength of interactions between particles. For this we use the so-called Gross-Pitaevskii-Newton system. In this context we especially determine the case of very high total masses where the ground state solutions of the Gross-Pitaevskii- Newton system can be approximated with the Thomas-Fermi limit. Furthermore, stability properties of the computed radially excited states are examined by applying arguments of the catastrophe theory.

Lagrange optimality system for a class of nonsmooth convex optimization

In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with the standard optimality condition and the saddle point condition of the augmented Lagrangian, which provides a powerful tool for developing numerical algorithms: we derive a Lagrange–Newton algorithm for the nonsmooth convex optimization, and establish the nonsingularity of the Newton system and the local convergence of the algorithm.

An interior point method designed for solving linear quadratic optimal control problems with hp finite elements

We consider linear quadratic optimal control problems with elliptic partial differential equations. The problem is solved with an interior point method in the control variable. We prove convergence of this method in function space by employing a suitable smoothing operator. As discretization we choose hp-finite element method based on local estimates on the smoothness of functions. A fully adaptive algorithm is implemented and a-posteriori error estimators are derived for the central path and the Newton system. The theoretical results are complemented by numerical examples.

The Schrödinger–Newton system with self-field coupling

We study the Schrödinger–Newton (SN) system of equations with the addition of gravitational field energy sourcing—such additional nonlinearity is to be expected from a theory of gravity (like general relativity (GR)), and its appearance in this simplified scalar setting (one of Einstein's precursors to GR) leads to significant changes in the spectrum of the self-gravitating theory. Using an iterative technique, we compare the mass dependence of the ground state energies of both SN and the new, self-sourced system and find that they are dramatically different. The Bohr method approach from old quantization provides a qualitative description of the difference, which comes from the additional nonlinearity introduced in the self-sourced case. In addition to comparison of ground state energies, we calculate the transition energy between the ground state and first excited state to compare emission frequencies between SN and the self-coupled scalar case.

A Hybrid Proximal Extragradient Self-Concordant Primal Barrier Method for Monotone Variational Inequalities

This paper presents a hybrid proximal extragradient (HPE) self-concordant primal barrier method for solving a monotone variational inequality over a closed convex set endowed with a self-concordant barrier and with an underlying map that has Lipschitz continuous derivative. In contrast to the iteration of a previous method developed by the first and third authors that has to compute an approximate solution of a linearized variational inequality, the one of the present method solves a simpler Newton system of linear equations. The method performs two types of iterations, namely, those that follow ever changing interior paths and those that correspond to large-step HPE iterations. Due to its first-order nature, the present method is shown to have a better iteration-complexity than its zeroth order counterparts such as Korpelevich's algorithm and Tseng's modified forward-backward splitting method, although its work per iteration is larger than the one for the latter methods.

Global solution of the electromagnetic field-particle system of equations

In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it generates. A unique solution is proved to exist (for regular charge distributions) on suitable homogeneous and non-homogeneous Sobolev spaces, for the electromagnetic field, and on coordinate and velocity space for the charge; provided initial data belong to the subspace that satisfies the divergence part of Maxwell's equations.

Extending the robustness and efficiency of artificial compressibility for partitioned fluid–structure interactions

In this paper we introduce the idea of combining artificial compressibility (AC) with quasi-Newton (QN) methods to solve strongly coupled, fully/quasi-enclosed fluid–structure interaction (FSI) problems. Partitioned, incompressible, FSI based on Dirichlet–Neumann domain decomposition solution schemes cannot be applied to problems where the fluid domain is fully enclosed. A simple example often provided in literature is that of a balloon with a prescribed inflow velocity. In this context, artificial compressibility (AC) is a useful method by which the incompressibility constraint can be relaxed by including a source term within the fluid continuity equation. The attractiveness of AC stems from the fact that this source term can readily be added to almost any fluid field solver, including most commercial solvers. Once included, both the modified fluid solver and structural solver can be treated as “black-box” field operators. AC is however limited to the class of problems it can effectively be applied to. For example, AC is an efficient solution strategy for the simulation of blood flow through arteries, but performs poorly when applied to the simulation of blood flow through an opening heart valve. The focus of this paper is thus to extend the application of AC by including an additional Newton system accounting for the missing interface sensitivities. We do so through the use of a multi-vector update quasi-Newton (MVQN) method, where the required system Jacobians are approximated rather than explicitly computed. In so doing, we continue to facilitate the notion that the AC modified fluid field solver and solid field solver can be treated as “black-box” solvers. We aim to demonstrate the improved performance of the combination of AC+QN when compared to AC applied in isolation.